The long-range objectives of this project are to understand dynamic pattern formation in reacting systems and to apply the results to specific problems of spatial pattern formation in developmental biology. The specific questions to be addressed are the following: (1) What are the minimal properties of the kinetic mechanism needed to produce stable pattern in an initially uniform system when transport occurs only by diffusion? by active transport? or, by a combination of these? (2) What conditions on the kinetics and the transport mechanism ensure pattern regulation? That is, when are the solutions of the governing equations invariant under certain changes of length and/or time scale and when can part of the pattern reproduce the whole? (3) What is the effect of pre-existing pattern on pattern formation and how might the succession from one pattern to another be controlled?